Follow-thorough. At the moment the shot occurs, the shooter should do the following:
The most important thing to do at the moment the trigger breaks is nothing. Nothing, nada, zilch, zero reaction, 'be a bag of sand', etc. etc. etc. All you have to do is wait until after the shot to flinch, blink, yawn, whatever. By then you can no longer affect the accuracy of the shot. Learning not to anticipate the shot, and to delay your reaction to the shot is the essence of marksmanship. It is a skill of the mind alone. To assist with training your mind to do your bidding the marksman should also perform the following steps.
Call the shot. Mentally, verbally, and/or in writing the location of the point of aim, at the moment of the shot, relative to the desired point of impact is recorded. A common way is to use angular measurement (MOA or MILS) combined with O'Clock. Thus a shot fired when the sights are to the right of the desired point of impact by 1” at 100 yds, would be 'called' as “1 MOA 3 O'Clock”. Focusing on 'calling your shot' will improve your shooting measurably.
Hold the trigger. The bullet will leave the barrel much faster than you can react to the noise and recoil, unfortunately the human mind knows how to anticipate. If your mind decides to react to the noise and recoil in any way, it will inevitably anticipate the event and react before the event occurs. This is the source of many if not all problems with shooter consistency and skill improvement. Maintaining the pressure used to fire the trigger (no more, no less) will help keep your mind focused on events after the shot, making it much easier to skip the anticipation.